Homology cylinders: an enlargement of the mapping class group

Jerome Levine

doi:10.2140/agt.2001.1.243

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Homology cylinders: an enlargement of the mapping class group

Jerome Levine

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Abstract

We consider a homological enlargement of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov-Habiro theory of finite-type invariants of 3-manifolds. We study the structure of this group from several directions: the relative weight filtration of Dennis Johnson, the finite-type filtration of Goussarov-Habiro, and the relation to string link concordance. We also consider a new Lagrangian filtration of both the mapping class group and the group of homology cylinders.

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Jerome Levine. 2000-10-26. Homology cylinders: an enlargement of the mapping class group. https://doi.org/10.2140/agt.2001.1.243

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